Econ 5

Which of the following is FALSE?

The sample size is an unbiased estimator of N.

Which of the following is NOT a property of joint probability distributions of discrete random variables?

a. P(x, y) can be greater than 1 for some pair of values x and y if and only if the sum of the joint probabilities P (x, y) over all possible pairs of values remains equal to 1

Which of the following is true about a sample proportion?

a. Since sample proportion is a mean, one can find the z-value and an acceptance interval.

If the covariance between two random variables is zero, then it is ALWAYS the case that:

a. The correlation coefficient is zero

A z-score equal to zero indicates that:

a. The value is equal to the mean

Which of the following is NOT true about a mode?

a. There is always a mode

Numerical data can be graphically represented by which of the following? If more than one answer is correct, please choose (d).

a.Line chart b.Scatter plot c.Histogram d.More than one answer is correct

Imagine you're entering a lottery in which the odds of winning are 1 to 4. What is the probability of winning?

b. 0.2

When you toss a coin, there are only two possible outcomes: heads and tails. The coin is NOT fair, and heads occur with a probability of 40 % and tails--with a probability of 60 %. Define a random variable X such that X = 1 if you obtain heads and X = 0 if you obtain tails. What is Var[X]?

b. 0.24

The variance of a uniform random variable with 4 as a minimum value and 6 as a maximum value is:

b. 1/3

Let X be a random variable such that Var(X) = 3. Find Var(6X)

b. 108

Consider the following data set: {24, 25, 32, 52, 27, 22, 2, 12, 72, 21}. If we want 5 classes, what is the interval width?

b. 14

Suppose four distinct books are to be arranged in order on a shelf. How many different orderings are possible?

b. 24

Imagine that, for your teaching assistant, the probability of drinking coffee in the morning is independent of whether they worked late the night before or not. The probability of having coffee in the morning is 40% and the probability of working late is 90%. What is the probability of drinking coffee in the morning given working late the night before?

b. 40%

Consider the following data set: {24, 25, 32, 52, 27, 22, 2, 12, 72, 21}. How many leaves does stem "2" have?

b. 5

The mean of a uniform random variable with 4 as a minimum value and 6 as a maximum value is:

b. 5

When the sample size is more than ___% of the population size (and sampling is without replacement) then a finite population correction factor must be used when calculating the standard error.

b. 5

Imagine that 1 in 5 individuals is allergic to peanuts. A peanut allergy test gives a positive result 10% of the time. If someone has a peanut allergy, the test will give a positive result 40% of the time. What is the probability that you have a peanut allergy if the test result is positive?

b. 80%

Imagine the critical value appropriate for this problem is 1.960. Which of the following t-statistics will lead us to reject the null hypothesis?I. 1.74II. 2.79III. 3.04

b. Both II and III

Imagine we want to calculate the confidence intervals for population variance. Which of the following statements is FALSE?

b. Chi-square distribution has n degrees of freedom.

A group of researchers are interested in obtaining the confidence interval for the mean difference in risk taking behavior between men and women. They have a sample of 51 men and 55 women and measure the risk taking behavior in a new scale that goes from 0 to 100. From the literature, they know that the variance between the choices of both groups is very similar. Which kind of problem represents this situation?

b. Difference in means with independent samples and equal unknown variance.

Which of the following is always true about a simple random sampling procedure?

b. Every object in the population has the same probability of being selected.

For a correlation coefficient of 0, what could the scatter plot of x and y look like?

b. Horizontal line

Which of the following is ALWAYS true about sample variance?

b. It has mean equal to the true variance.

Which of the following is NOT true about the level of significance of a test?

b. It is designated by e

You want to plot the number of marriages in the US per year from 2000 to 2021. Which graph should you use?

b. Line chart

Which of the following information is NOT included on a box and whisker plot?

b. Mean

Which of the following conditions ensures that a distribution is symmetric?

b. Median = Mean

Which of the following provides a correct definition of the p-value?

b. Probability of obtaining a test statistic more extreme than the observed sample value given that the null hypothesis is true.

Which of the following best describes the margin of error?

b. Upper confidence limit - Point estimate

What are the degrees of freedom of a t distribution used to calculate the margin of error in a confidence interval for the difference between two means when the samples are independent, and the variances are unknown but assumed equal?

b. nx+ny-2

Imagine P(A) = 0.25, P(B) =0.8, and A and B are statistically independent. What is the probability of the intersection of A and B

c. 0.2

Imagine P(A) = 0.3, P(B) =0.2, and A and B are mutually exclusive. What is the probability of the union of A and B

c. 0.5

Let X be a random variable such that Var(X) = 169. Find the standard deviation of X

c. 13

What is the median of the following data set: 8, 10, 4, 4, 6, 8, 2?

c. 6

Which of the following null hypothesis would be most appropriately tested using a two-tailed test?

c. Average height of Isla Vista residents is 5'6.

Consider the following statements about the standard error of the mean: is a measure of the variability in the mean from sample to sample. Decreases as the sample size increases. Which of the above statements is correct? If both statements are correct, pick answer (C).

c. Both (I) and (II)

Which of the following is plotted on the vertical axis of a histogram?

c. Frequency

Which of the following statements is FALSE?

c. If Y follows a normal distribution, then Y can only take positive values.

Under which conditions can we say for sure that two random variables X and Y are independent?

c. If the joint cumulative distribution function F(x,y) is equal to the product of their marginal distribution functions F(x) F(y).

Which of the following is an example of a discrete numerical variable?

c. Number of customers that visited Woodstock pizza today

Consider the following two data sets. Data set 1: 28, 22, 25, 24, 98, 21, 21 Data set 2: 97, 98, 100, 88, 20, 21, 95 What can you say about the ranges of these data sets?

c. Range of data set 1 is smaller than the range of data set 2

What is the 99% confidence interval for the difference between two means with dependent samples when the mean of the differences is d=-4, the sd=10, and the sample size was 25?

d. (-9.59, 1.59)

The finite population correction factor formula is:

d. (N-n)/(N-1)

Let the Sample Space be the collection of all possible outcomes of rolling one die: S = [1, 2, 3, 4, 5, 6]. Which of the two events are mutually exclusive?

d. A = [1, 2], B = [5, 6]

According to the syllabus, which of the following is FALSE about the in-person lecture activities?

d. All 9 activity scores are included in the final course grade calculation

Which of the following examples is NOT a dependent sample:

d. Comparing the performance of students from two different high schools on SAT

The standardized random variable z has

d. Mean 0 and variance 1

If Cov(x,y) =0, then:

d. None of the above

Which of the following statements is correct?

d. None of the above

Consider a population of four individuals. Which of the following is true?

d. None of the above.

The conditional probability function of X, given Y = y is defined as:

d. P(x, y) / P (y)

Within the decision rule framework, which of the following pairs of p-value and α will result in rejection of the null hypothesis?

d. P-value = 0.03; = 0.05.

We use a t statistic when:

d. Population variance is not known.

How do we define the power of a test?

d. Probability of rejecting a null hypothesis that is false.

Which of the following is TRUE about type II error?

d. Probability of type II error decreases when the probability of type I error increases.

In the formula for the normal probability density function, (mew) stands for:

d. The population mean

When is a finite population correction necessary?

d. When the sample size n is not a small fraction of the population size N.

When is the normal distribution is a good approximation of the binomial distribution?

d. Whenever nP(1-P) > 5, where n is the number of trials and P is the probability of success on any given trial

Consider A= [1, 2, 3, 5, 6] and B = [3, 4, 5, 7, 8]. Which is the intersection of A and B?

d. [ 3, 5]

Eye color is an example of _________ data and height is an example of _________ data.

d. categorical; continuous numerical

Which of the following is true?

d. t value is used when is sigma^2 unknown

According to Bayes' Rule, P(A|B) equals which of the following?

(P(B|A) * P(A)) / P(B)

Consider the random sample X1, X2, ... Xn . The sample mean is defined as:

(X1+ X2+ ... + Xn)/ n

When estimating the confidence interval of the mean difference between two independent samples and their variances are unknown but equal. The formula for the pooled samples variance is:

(nx-1)s^2x+(ny-1)s^2y / nx+ny-2

If the confidence level is 90%, then the value of alpha is:

10%

Suppose the true value of a parameter is 8, the expected value of the point estimator of this parameter is 10, then the bias in this estimator is:

2

Suppose you have a list of 5 students from a history class. 2 of them come from California, 2 from Arizona, and 1 from Kansas. In a pie chart:

40 % of the surface would be of a color that represents California, 40% would be of a different color that represents Arizona and 20 % would be of a different color that represents Kansas

Which of the following examples doesn't correspond to a problem of inference to estimate certain parameters of two populations when the sample is independent:

A firm executive wants to compare sales before and after restructuring of the sales department

The goal of the calculating an acceptance interval is to:

Determine a range within which sample means are likely to occur, given a population mean and variance.

Which of the following is NOT true about a correlation coefficient?

Ranges normalized between 0 and 1

Which of the following is a correct formation of the t statistic?

a. (x-U)/(s/rootn)

A random sample of 80 high school students consists of 30 students taking the SAT. Form a 95% confidence interval for the true proportion of students taking the SAT. What is the lower tail of this interval? Pick the closest answer.

a. 0.3

A random sample of 80 high school students consists of 30 students taking the SAT. Form a 95% confidence interval for the true proportion of students taking the SAT. What is the upper tail of this interval? Pick the closest answer.

a. 0.5

If the area under the curve f(x) represents probability, then the total area under the curve f(x) equals:

a. 1

Commonly used confidence level 95% corresponds to which of the following z values?

a. 1.96

Let X be a random variable such that E(X) = 2.5. Find E(0.5 + 3X)

a. 8

Which of the following is NOT always true?

a. If the covariance between two random variables is 0, then these random variables are statistically independent

Consider a standard normal distribution. The z-value for the sampling distribution of the mean:

a. Is a standardized normal random variable with mean of 0 and a variance of 1.

Which of the following is NOT true about Bernoulli distribution?

a. Mean and variance of the Bernoulli distribution are always equal to Binomial distribution

Which of the following CANNOT be modelled by a Bernoulli probability distribution?

a. Number of trades an investor makes in a day